Relationship between Norm-internalization and Cooperation in N-person Prisoners' Dilemma Games

Abstract

In this paper, I discuss the problems of "order in social situations" using a computer simulation of iterated N-person prisoners' dilemma game. It has been claimed that, in the case of the 2-person prisoners' dilemma, repetition of games and the reciprocal use of the "tit-for- tat" strategy promote the possibility of cooperation. However, in cases of N-person prisoners' dilemma where N is greater than 2, the logic does not work effectively. The most essential problem is so called "sanctioning problems". In this paper, firstly, I discuss the "sanctioning problems" which were introduced by Axelrod and Keohane in 1986. Based on the model formalized by Axelrod, I propose a new model, in which I added a mechanism of players ' payoff changes in the Axelrod;s model. I call this mechanism norm-internalization and call our model "norm-internalization game". Second, by using the model, I investigated the relationship between agents' norm-internalization (payoff-alternation) and the possibilities of cooperation. The results of computer simulation indicated that unequal distribution of cooperating norm and uniform distribution of sanctioning norm are more effective in establishing cooperation. I discuss the mathematical features and the implications of the results on social science.